Choose the best selection for the
quadrilateral with vertices at the
following points:
(0,0), (3,2), (6,0), (3,-2)
Hint: Start by graphing the points.
Distance Formula: d= V(x2-x1)2 + (y2 - y1)2
A. Rectangle
B. Square
C. Rhombus
D. Trapezoid

Question

contestada

Respuesta :

MrRoyal MrRoyal · Answer 1 · 2021-12-30T13:35:42+01:00

The quadrilateral with vertices at the points: (0,0), (3,2), (6,0), (3,-2) is a square

The vertices (or coordinates) of the quadrilateral is given as:

[tex](x,y) = (0,0), (3,2), (6,0), (3,-2)[/tex]

Calculate the distance between subsequent points, using the following distance formula

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

So, we have:

[tex]AB = \sqrt{(0 -3)^2 + (0 -2)^2}[/tex]

[tex]AB = \sqrt{13}[/tex]

[tex]BC = \sqrt{(3 -6)^2 + (2 -0)^2}[/tex]

[tex]BC = \sqrt{13}[/tex]

[tex]CD = \sqrt{(6 -3)^2 + (0 --2)^2}[/tex]

[tex]CD = \sqrt{13}[/tex]

[tex]DA = \sqrt{(3 -0)^2 + (-2 -0)^2}[/tex]

[tex]DA = \sqrt{13}[/tex]

Notice that the sides of the quadrilateral are congruent.

Hence, the quadrilateral is a square